A course in computational algebraic number theory
A course in computational algebraic number theory
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Remote timing attacks are practical
SSYM'03 Proceedings of the 12th conference on USENIX Security Symposium - Volume 12
Twisted Edwards Curves Revisited
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Exponent Recoding and Regular Exponentiation Algorithms
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Efficient 3-dimensional GLV method for faster point multiplication on some GLS elliptic curves
Information Processing Letters
Efficient techniques for high-speed elliptic curve cryptography
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
Journal of Cryptology
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
High-speed high-security signatures
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Designs, Codes and Cryptography
Fast elliptic curve cryptography in OpenSSL
FC'11 Proceedings of the 2011 international conference on Financial Cryptography and Data Security
Faster implementation of scalar multiplication on koblitz curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Lambda coordinates for binary elliptic curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
High-Performance scalar multiplication using 8-dimensional GLV/GLS decomposition
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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The GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) computes any multiple kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ (called GLV curve) over $\mathbb{F}_p$ as $kP = k_1P + k_2\Phi(P), \text{with } \max\{|k_1|,|k_2|\}\leq C_1\sqrt n$, for some explicit constant C10. Recently, Galbraith, Lin and Scott (EUROCRYPT 2009) extended this method to all curves over $\mathbb{F}_{p^2}$ which are twists of curves defined over $\mathbb{F}_p$. We show in this work how to merge the two approaches in order to get, for twists of any GLV curve over $\mathbb{F}_{p^2}$, a four-dimensional decomposition together with fast endomorphisms Φ, &Ψ over $\mathbb{F}_{p^2}$ acting on the group generated by a point P of prime order n, resulting in a proven decomposition for any scalar k∈[1,n] given by kP=k1P+k2Φ(P)+k3&Ψ(P)+k4&ΨΦ(P) with max i (|ki|)C2n1/4, for some explicit C20. Remarkably, taking the best C1, C2, we obtain C2/C1